OPERATOR EXPONENTS OF PROBABILITY-MEASURES AND LIE SEMIGROUPS

• 成果类型: Article
• 署名作者: JUREK, ZJ
• 署名单位: University of Wroclaw
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176989817
• 发表日期: 1992
• 页码: 1053-1062
• 关键词: spaces

摘要

A notion of U-exponents of a probability measure on a linear space is introduced. These are bounded linear operators and it is shown that the set of all U-exponents forms a Lie wedge for full measures on finite-dimensional spaces. This allows the construction of U-exponents commuting with the symmetry group of a measure in question. Then the set of all commuting exponents is described and elliptically symmetric measures are characterized in terms of their Fourier transforms. Also, self-decomposable measures are identified among those which are operator-self-decomposable. Finally, S-exponents of infinitely divisible measures are discussed.